{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4UTNNSBMOICPGH76KGW2YT32OU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6edc0b02f2648dd516f2c40acd30d6d2ed7393e6fcadc4a47a2f4b417eb915f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T23:02:06Z","title_canon_sha256":"69725efb0d9c60b5b3676146dc77dbef8e40a4ac736634adcb45dc2f06ce7d42"},"schema_version":"1.0","source":{"id":"1603.05723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05723","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05723v1","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05723","created_at":"2026-05-18T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"4UTNNSBMOICP","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4UTNNSBMOICPGH76","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4UTNNSBM","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:465c8e971faf851e87a2efcd48c9d6492201d490a0d7dfe0a8cebe26fef1d152","target":"graph","created_at":"2026-05-18T01:18:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the three-dimensional cubic nonlinear Schr\\\"odinger system\n  \\begin{equation*} \\begin{cases} i\\partial_tu+\\Delta u+(|u|^2+\\beta |v|^2)u=0,\\\\ i\\partial_tv+\\Delta v+(|v|^2+\\beta |u|^2)v=0. \\end{cases} \\end{equation*} Let $(P,Q)$ be any ground state solution of the above Schr\\\"odinger system. We show that for any initial data $(u_0,v_0)$ in $H^1(\\mathbb{R}^3)\\times H^1(\\mathbb{R}^3)$ satisfying $M(u_0,v_0)A(u_0,v_0)<M(P,Q)A(P,Q)$ and $M(u_0,v_0)E(u_0,v_0)<M(P,Q)E(P,Q)$, where $M(u,v)$ and $E(u,v)$ are the mass and energy (invariant quantities) associated to the system, the correspondi","authors_text":"Ademir Pastor, Luiz Gustavo Farah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T23:02:06Z","title":"Scattering for a 3D coupled nonlinear Schr\\\"odinger system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05723","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5c5d20a6e730bba1f025228b158328f7b446909502f26546a4dfcb03f41481a0","target":"record","created_at":"2026-05-18T01:18:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6edc0b02f2648dd516f2c40acd30d6d2ed7393e6fcadc4a47a2f4b417eb915f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-17T23:02:06Z","title_canon_sha256":"69725efb0d9c60b5b3676146dc77dbef8e40a4ac736634adcb45dc2f06ce7d42"},"schema_version":"1.0","source":{"id":"1603.05723","kind":"arxiv","version":1}},"canonical_sha256":"e526d6c82c7204f31ffe51adac4f7a750c8a792f0d8b3dfaae415ed470988752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e526d6c82c7204f31ffe51adac4f7a750c8a792f0d8b3dfaae415ed470988752","first_computed_at":"2026-05-18T01:18:53.679607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:53.679607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/dsBDe9VDCME5CxRpz8DE4oXvBcHywCQJNWpIuakOCPnINaftr8WPBRcrb8ZY0dYnj+LNoKtml0hT/ttYDtoAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:53.680112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c5d20a6e730bba1f025228b158328f7b446909502f26546a4dfcb03f41481a0","sha256:465c8e971faf851e87a2efcd48c9d6492201d490a0d7dfe0a8cebe26fef1d152"],"state_sha256":"383e2b875145b892d55866e4e5af2ff63fae30f0d022eb15d64226bd26edc7fc"}